In signal processing

Signal processing

Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

, a recursive filter is a type of filter

Filter (signal processing)

In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...

 which re-uses one or more of its outputs as an input. This feedback

Feedback

Feedback describes the situation when output from an event or phenomenon in the past will influence an occurrence or occurrences of the same Feedback describes the situation when output from (or information about the result of) an event or phenomenon in the past will influence an occurrence or...

 typically results in an unending impulse response

Impulse response

In signal processing, the impulse response, or impulse response function , of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change...

 (commonly referred to as infinite impulse response

Infinite impulse response

Infinite impulse response is a property of signal processing systems. Systems with this property are known as IIR systems or, when dealing with filter systems, as IIR filters. IIR systems have an impulse response function that is non-zero over an infinite length of time...

(IIR

IIR

IIR may refer to* IIR Holdings, a human capital development company acquired by Informa* Indo-Iranian languages* Infinite impulse response...

)), characterised by either exponentially growing

Exponential growth

Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...

, decaying, or sinusoidal signal output components.

However, a recursive filter does not always have an infinite impulse response. Some implementations of moving average filter are recursive filters but with a Finite impulse response.